General manager Steve Yzerman said he doesn't expect Callahan to be ready for the start of training camp.
Callahan, 33, said in exit interviews that he had been playing with the injury down the stretch of the season. He missed a couple of playoff games after aggravating the injury.
Callahan just wrapped up his fifth season in Tampa Bay, collecting 5 goals and 13 assists. He's under contract for the next two seasons.